May police enter my private property without someone calling them?

If you have posted No Tresspassing signs on your property,
then the police typically may only come on your property if they have probable cause to
do so.

In order for the police to come on your property,
they must have a good reason to do so.  For example, if they are serving you a warrant,
they have the right to come on your property.  If they have probable cause to believe
that a crime has been or is being committed on your property, they have a right to enter
the property.  If they have probable cause to believe that you are witness to a crime,
they can probably come on your property.

The laws on this
vary from place to place, but the police generally have a right to enter private
property on official business if they believe there is a need to do
so.